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A strong converse shows that no procedure can beat the asymptotic (as blocklength $n\to\infty$) fundamental limit of a given information-theoretic problem for any fixed error probability. A second-order converse strengthens this conclusion…

Information Theory · Computer Science 2019-11-18 Jingbo Liu , Ramon van Handel , Sergio Verdú

In this paper, we establish novel data-dependent upper bounds on the generalization error through the lens of a "variable-size compressibility" framework that we introduce newly here. In this framework, the generalization error of an…

Machine Learning · Statistics 2024-06-12 Milad Sefidgaran , Abdellatif Zaidi

It is well known that the empirical likelihood ratio confidence region suffers finite sample under-coverage issue, and this severely hampers its application in statistical inferences.} The root cause of this under-coverage is an upper limit…

Methodology · Statistics 2021-08-16 Guangxing Wang , Wolfgang Polonik

We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length…

Quantum Physics · Physics 2009-01-19 Markus Mueller , Caroline Rogers , Rajagopal Nagarajan

The paper derives the optimal second-order coding rate for the continuous-time Poisson channel. We also obtain bounds on the third-order coding rate. This is the first instance of a second-order result for a continuous-time channel. The…

Information Theory · Computer Science 2020-08-18 Yuta Sakai , Vincent Y. F. Tan , Mladen Kovačević

In this paper, we consider the problem of variable-length source coding allowing errors. The exponential moment of the codeword length is analyzed in the non-asymptotic regime and in the asymptotic regime. Our results show that the smooth…

Information Theory · Computer Science 2015-12-22 Shigeaki Kuzuoka

We consider the first-order theory of random variables with the probabilistic independence relation, which concerns statements consisting of random variables, the probabilistic independence symbol, logical operators, and existential and…

Information Theory · Computer Science 2021-08-18 Cheuk Ting Li

We derive high-order terms in the asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. Our…

Mathematical Physics · Physics 2007-05-23 Habib Ammari , Hyeonbae Kang

We study variable-length codes for point-to-point discrete memoryless channels with noiseless unlimited-rate feedback that occurs in $L$ bursts. We term such codes variable-length bursty-feedback (VLBF) codes. Unlike classical codes with…

Information Theory · Computer Science 2023-06-27 James Y. Chen , Recep Can Yavas , Victoria Kostina

We consider a family of linear viscoelastic shells with thickness $2\varepsilon$ ( $\varepsilon$ , small parameter), clamped along a portion of their lateral face, all having the same middle surface $S$. We formulate the three-dimensional…

Analysis of PDEs · Mathematics 2017-02-16 G. Castiñeira , Á. Rodríguez-Arós

The exact order of the optimal sub-exponentially decaying factor in the classical bounds on the error probability of fixed-length codes over a Gallager-symmetric discrete memoryless channel with and without ideal feedback is determined.…

Information Theory · Computer Science 2019-09-02 Yücel Altuğ , Aaron B. Wagner

We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…

Computer Vision and Pattern Recognition · Computer Science 2015-05-05 Alexander Shekhovtsov

The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…

Methodology · Statistics 2025-05-02 Elena Bortolato , Francesco Bertolino , Monica Musio , Laura Ventura

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…

Optimization and Control · Mathematics 2021-05-31 C. Cartis , N. I. M. Gould , Ph. L. Toint

We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding a variable-length uniform random number, and the asymptotically minimum average length rate of the…

Information Theory · Computer Science 2017-01-31 Hideki Yagi , Te Sun Han

Given a finite alphabet $A$, a quasi-metric $d$ over $A^*$, and a non-negative integer $k$, we introduce the relation $\tau_{d,k}\subseteq A^*\times A^*$ such that $(x,y)\in\tau_{d,k}$ holds whenever $d(x,y)\le k$. The error detection…

Discrete Mathematics · Computer Science 2023-09-06 Jean Néraud

In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…

Information Theory · Computer Science 2009-03-06 Michael B. Baer

A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…

Information Theory · Computer Science 2021-11-29 Sebastian Espinosa , Jorge F. Silva , Pablo Piantanida

Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…

Statistics Theory · Mathematics 2023-11-21 Soham Mallick , Siddhaarth Sarkar , Arun Kumar Kuchibhotla

We consider the problems ZERO EXTENSION and METRIC LABELLING under the paradigm of parameterized complexity. These are natural, well-studied problems with important applications, but have previously not received much attention from…

Data Structures and Algorithms · Computer Science 2018-02-19 Felix Reidl , Magnus Wahlström